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Nature of Roots

The roots of ...

Question

The roots of the equation px^2-2(p+2)x+3p=0 are alpha and beta .If alpha- beta=2, calculate the value of Alpha, beta and p

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α

β

are the roots of the equation

3 x^{2} - 2 x - 8 = 0

, find the value of

α^{2} - α β + β^{2}

.

α

β

are the roots of the quadratic equation

x^{2} + (p - 3) x - 2 p = 3

(p \in R)

, then the minimum value of

(α^{2} + β^{2} + α β)

α, β

are the roots of the equation

x^{2} - 2 x + 3 = 0

. Then the equation whose roots are

P = α^{3} - 3 α^{2} + 5 α - 2

Q = β^{3} - β^{2} + β + 5

α

β

are roots of the quadratic equation

2 p^{2} x^{2} + 2 p^{3} x - 1 = 0, p \in R - 0

, then minimum value of

α^{4} + β^{4}

α, β

are the zeroes of

f (x) = p x^{2} - 2 x + 3 p

α + β = α β,

then the value of

p

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